Osasuna fared badly in the match against Deportivo. (Getty Images)
Barcelona: Deportivo Coruna beat Osasuna 2-0 in their return to Spain's topflight thanks to second-half goals by forwards Ivan "Riki" Sanchez and Nelson Oliviera on Monday.
Riki made up for a missed penalty by scoring in the 53rd, and Oliveira, a young Portugal prospect, sealed the win at Riazor stadium in injury time with a superb individual effort.
Also, Roberto Trashorras scored from a free kick deep into stoppage time to give Rayo Vallecano coach Paco Jemez a 1-0 win over Granada in his the debut.
In Monday's late game, newly promoted Valladolid won 1-0 at Zaragoza to close out round one.
While Osasuna carried the weight of play in the first half, it was Deportivo who had the best chances to go ahead.
Luis "Pizzi" Afonso hit the crossbar in the seventh minute, and Riki sent a spot kick off the post, squandering the chance from Miguel Flano's foul of Bruno Gama in the area.
Riki compensated for his miss in the 53rd when he raced down the right flank, cut back and fired between the near post and goalkeeper Andres Fernandez.
Oliviera went on for Riki in the 64th to debut in the Spanish league after arriving on loan this offseason from Benfica.
The 21 year old, who played for Portugal in the European championships, scored two minutes into stoppage time when he ran onto a long pass, rode his defender and coolly chipped over Fernandez.
"I am satisfied more with how we played than with the result," said coach Jose Oltra, who led Deportivo back from the second division after one season.
"The team played with a clear idea of what we wanted to do," he said. "There are still some things to work on, but we are on the right course."
After 94 minutes of rough-and-tumble football, Rayo and Granada looked destined to share the points until Rayo earned a free kick with injury time almost expired. Trashorras did not waste his team's last chance as the midfielder curled the ball over the defensive wall and beyond the outstretched goalkeeper to claim the win for the hosts in dramatic fashion.
Despite the victory, Jemez said he was not completely satisfied with how his team played in what was overall a sloppy affair for both sides.
"In the first half we played well, but in the second we lost control of the game and made mistakes that allowed (Granada) to press forward," he said. "The win will help us think in a humble way about what we need to do to stay up this season."
After resisting Zaragoza's initial surge, Valladolid went ahead at La Romareda stadium one minute before halftime by executing a counterattack to perfection. Forward Oscar Gonzalez played Omar Ramos wide to the left and then charged forward into the area to knock his low cross past goalkeeper Roberto Jimenez.
Jimenez saved a penalty later to keep Zaragoza in the game, but the visitors held on for the win.
"We played well and leave with good sensations," said Gonzalez, a former Zaragoza player. "We know we need to work more in defense and that it will be tough this season, but we also know that if we play well we'll get good results."
On Sunday, Barcelona thrashed Real Sociedad 5-1 in coach Tito Vilanova's first game after replacing Pep Guardiola following five seasons as his assistant. Defending champions Real Madrid drew 1-1 at home with Valencia, while Real Betis won 5-3 at Athletic Bilbao and Atletico Madrid drew 1-1 at Levante.
On Saturday, it was: Celta Vigo 0, Malaga 1; Sevilla 2, Getafe 1; and Mallorca 2, Espanyol 1.